On the monotonization of the training set

Details On the monotonization of the training set On the monotonization of the training set

2007-05-18

arxiv.org/abs/0705.2765v1

Computer Science

Learning

10 pages

Scientific paper

We consider the problem of minimal correction of the training set to make it consistent with monotonic constraints. This problem arises during analysis of data sets via techniques that require monotone data. We show that this problem is NP-hard in general and is equivalent to finding a maximal independent set in special orgraphs. Practically important cases of that problem considered in detail. These are the cases when a partial order given on the replies set is a total order or has a dimension 2. We show that the second case can be reduced to maximization of a quadratic convex function on a convex set. For this case we construct an approximate polynomial algorithm based on convex optimization.

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